von Neumann neighborhood
E656652
The von Neumann neighborhood is a grid-based notion of adjacency in cellular automata and lattice models where each cell interacts only with the four orthogonally adjacent cells (up, down, left, right).
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
concept in cellular automata theory
ⓘ
local neighborhood structure ⓘ neighborhood (cellular automata) ⓘ |
| canBeExtendedTo | higher-dimensional lattices ⓘ |
| contrastsWith | Moore neighborhood NERFINISHED ⓘ |
| correspondsTo | 4-connectedness in digital topology ⓘ |
| definedOn |
regular grid
ⓘ
square lattice ⓘ |
| excludesAdjacencyType | diagonal adjacency ⓘ |
| generalizesTo | von Neumann neighborhood of radius r ⓘ |
| hasAdjacencyType | orthogonal adjacency ⓘ |
| hasAlternativeName | 4-neighborhood ⓘ |
| hasCardinality | 4 (in 2D, radius 1) ⓘ |
| hasDimension | 2 (standard case) ⓘ |
| hasFewerNeighborsThan | Moore neighborhood (in 2D, radius 1) ⓘ |
| hasGraphTheoreticInterpretation | neighbors in the 2D grid graph ⓘ |
| hasNeighborDirection |
down
ⓘ
left ⓘ right ⓘ up ⓘ |
| hasRadius | 1 (standard definition) ⓘ |
| hasSymmetryGroup | dihedral group of the square (D4) in 2D ⓘ |
| inducesMetric | Manhattan distance (L1 metric) NERFINISHED ⓘ |
| inHigherDimensionsHasCardinality | 2d (for dimension d, radius 1) ⓘ |
| isCommonDefaultIn | early cellular automata models ⓘ |
| isIsotropicWithRespectTo | Manhattan distance ⓘ |
| isLocal | true ⓘ |
| isSubsetOf | Moore neighborhood (for same radius in 2D) NERFINISHED ⓘ |
| isTranslationInvariantOn | regular lattices ⓘ |
| namedAfter | John von Neumann NERFINISHED ⓘ |
| usedFor |
defining connectivity in grid graphs
ⓘ
defining local update rules in cellular automata ⓘ modeling diffusion on grids ⓘ modeling nearest-neighbor interactions ⓘ |
| usedIn |
Ising model on a square lattice (nearest-neighbor version)
NERFINISHED
ⓘ
cellular automata ⓘ discrete dynamical systems ⓘ grid-based simulations ⓘ image processing ⓘ lattice gas automata ⓘ lattice models ⓘ percolation theory NERFINISHED ⓘ reaction-diffusion cellular automata ⓘ statistical mechanics models ⓘ |
| wasIntroducedInContextOf | von Neumann’s work on self-reproducing automata ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.